Electromagnetic theory

Front Matter......Page 1
Appendices......Page 0
Foreword......Page 3
Introduction......Page 5
Preface......Page 10
Table of Contents......Page 14
1.1.1 The Field Vectors......Page 21
1.1.2 Charge and Current......Page 22
1.1.4 Integral Form of the Field Equations......Page 26
1.2.1 The Inductive Capacities epsilon and mu......Page 30
1.2.2 Electric and Magnetic Polarization......Page 31
1.2.3 Conducting Media......Page 33
1.3.1 The M.K.S. or Giorgi System......Page 36
1.4.1 Vector and Scalar Potentials......Page 43
1.4.2 Homogeneous Conducting Media......Page 46
1.4.3 The Hertz Vectors, or Polarization Potentials......Page 48
1.4.4 Complex Field Vectors and Potentials......Page 52
1.5.1 Discontinuities in the Field Vectors......Page 54
1.6.1 Unitary and Reciprocal Vectors......Page 58
31534_01b......Page 60
1.6.2 The Differential Operators......Page 64
1.6.3 Orthogonal Systems......Page 67
1.6.4 The Field Equations in General Orthogonal Coordinates......Page 70
1.6.5 Properties of Some Elementary Systems......Page 71
1.7.1 Orthogonal Transformations and Their Invariants......Page 79
1.7.2 Elements of Tensor Analysis......Page 84
1.7.3 The Space-Time Symmetry of the Field Equations......Page 89
1.7.4 The Lorentz Transformation......Page 94
1.7.5 Transformation of the Field Vectors to Moving Systems......Page 98
2.1.1 The Elastic Stress Tensor......Page 103
2.1.2 Analysis of Strain......Page 107
2.1.3 Elastic Energy and the Relations of Stress to Strain......Page 113
2.2.1 Definition of the Vectors E and B......Page 116
2.2.2 The Electromagnetic Stress Tensor in Free Space......Page 117
2.2.3 Electromagnetic Momentum......Page 123
2.3.1 Electrostatic Energy as a Function of Charge Density......Page 124
2.3.2 Electrostatic Energy as a Function of Field Intensity......Page 127
2.3.3 A Theorem on Vector Fields......Page 131
2.3.4 Energy of a Dielectric Body in an Electrostatic Field......Page 132
2.3.5 Thomson\'s Theorem......Page 134
2.3.6 Earnshaw\'s Theorem......Page 136
2.3.7 Theorem on the Energy of Uncharged Conductors......Page 137
2.4.1 Magnetic Energy of Stationary Currents......Page 138
2.4.2 Magnetic Energy as a Function of Field Intensity......Page 143
31534_02b......Page 144
2.4.3 Ferromagnetic Materials......Page 145
2.4.4 Energy of a Magnetic Body in a Magnetostatic Field......Page 146
2.4.5 Potential Energy of a Permanent Magnet......Page 149
2.5.1 Poynting\'s Theorem......Page 151
2.5.2 The Complex Poynting Vector......Page 155
2.6.1 Body Forces in Fluids......Page 157
2.6.2 Body Forces in Solids......Page 160
2.6.3 The Stress Tensor......Page 166
2.6.4 Surfaces of Discontinuity......Page 167
2.6.5 Electrostriction......Page 169
2.6.6 Force on a Body Immersed in a Fluid......Page 171
2.7.1 Nonferromagnetic Materials......Page 173
2.7.2 Ferromagnetic Materials......Page 175
2.8.1 Force on a Body Immersed in a Fluid......Page 176
3.1.1 Equations of Field and Potential......Page 180
3.1.2 Boundary Conditions......Page 183
3.2.1 Green\'s Theorem......Page 185
3.2.2 Integration of Poisson\'s Equation......Page 186
3.2.3 Behavior at Infinity......Page 187
3.2.4 Coulomb Field......Page 189
3.2.5 Convergence of Integrals......Page 190
3.3.1 Axial Distributions of Charge......Page 192
3.3.2 The Dipole......Page 195
3.3.3 Axial Multipoles......Page 196
3.3.4 Arbitrary Distributions of Charge......Page 198
3.3.5 General Theory of Multipoles......Page 199
3.4.1 Interpretation of the Vectors P and Pi......Page 203
3.5.1 Volume Distributions of Charge and Dipole Moment......Page 205
3.5.2 Single-Layer Charge Distributions......Page 207
3.5.3 Double-Layer Distributions......Page 208
3.5.4 Interpretation of Green\'s Theorem......Page 212
3.5.5 Images......Page 213
3.6.1 Formulation of Electrostatic Problems......Page 214
3.6.2 Uniqueness of Solution......Page 216
3.6.3 Solution of Laplace\'s Equation......Page 217
3.7.1 Conducting Sphere in Field of a Point Charge......Page 221
3.7.2 Dielectric Sphere in Field of a Point Charge......Page 224
3.7.3 Sphere in a Parallel Field......Page 225
3.8.1 Free Charge on a Conducting Ellipsoid......Page 227
3.8.2 Conducting Ellipsoid in a Parallel Field......Page 229
3.8.3 Dielectric Ellipsoid in Parallel Field......Page 231
3.8.4 Cavity Definitions of E and D......Page 233
3.8.5 Torque Exerted on an Ellipsoid......Page 235
Problems......Page 237
4.1.1 Field Equations and the Vector Potential......Page 245
4.1.2 The Scalar Potential......Page 246
4.1.3 Poisson\'s Analysis......Page 248
4.2.1 The Biot-Savart Law......Page 250
4.2.2 Expansion of the Vector Potential......Page 253
4.2.3 The Magnetic Dipole......Page 256
4.2.4 Magnetic Shells......Page 257
4.3.1 Fundamental Systems......Page 258
4.3.2 Coulomb\'s Law for Magnetic Matter......Page 261
4.4.1 Equivalent Current Distributions......Page 262
4.4.2 Field of Magnetized Rods and Spheres......Page 263
4.5.1 Surface Distributions of Current......Page 265
4.5.2 Surface Distributions of Magnetic Moment......Page 267
4.6.2 Application to the Vector Potential......Page 270
4.7.1 Formulation of the Magnetostatic Problem......Page 274
4.7.2 Uniqueness of Solution......Page 276
4.8.1 Field of a Uniformly Magnetized Ellipsoid......Page 277
4.9.1 Calculation of the Field......Page 278
4.9.2 Force Exerted on the Cylinder......Page 281
Problems......Page 282
5.1.1 Equations of a One-Dimensional Field......Page 288
5.1.2 Plane Waves Harmonic in Time......Page 293
5.1.3 Plane Waves Harmonic in Space......Page 298
5.1.4 Polarization......Page 299
5.1.5 Energy Flow......Page 301
5.1.6 Impedance......Page 302
5.2 General Solutions of the One-Dimensional Wave Equation......Page 304
5.2.1 Elements of Fourier Analysis......Page 305
5.2.2 General Solution of the One-Dimensional Wave Equation in a Nondissipative Medium......Page 312
5.2.3 Dissipative Medium; Prescribed Distribution in Time......Page 317
5.2.4 Dissipative Medium; Prescribed Distribution in Space......Page 321
5.2.5 Discussion of a Numerical Example......Page 324
5.2.6 Elementary Theory of the Laplace Transformation......Page 329
31534_05b......Page 332
5.2.7 Application of the Laplace Transform to Maxwell\'s Equations......Page 338
5.3.1 Dispersion in Dielectrics......Page 341
5.3.2 Dispersion in Metals......Page 345
5.3.3 Propagation in an Ionized Atmosphere......Page 347
5.4.1 Group Velocity......Page 350
5.4.2 Wave Front and Signal Velocities......Page 353
Problems......Page 360
6.1.1 Representation by Hertz Vectors......Page 369
6.1.2 Scalar and Vector Potentials......Page 371
6.1.3 Impedances of Harmonic Cylindrical Fields......Page 374
6.2.1 Elementary Waves......Page 375
6.2.2 Properties of the Functions Z_p (rho)......Page 377
6.2.3 The Field of Circularly Cylindrical Wave Functions......Page 380
6.3.1 Construction from Plane Wave Solutions......Page 381
6.3.2 Integral Representations of the Functions Z_n (rho)......Page 384
6.3.3 Fourier-Bessel Integrals......Page 389
6.3.4 Representation of a Plane Wave......Page 391
6.3.5 The Addition Theorem for Circularly Cylindrical Waves......Page 392
6.4.1 Elementary Waves......Page 395
6.4.2 Integral Representations......Page 400
6.4.3 Expansion of Plane and Circular Waves......Page 404
Problems......Page 407
7.1.1 A Fundamental Set of Solutions......Page 412
7.1.2 Application to Cylindrical Coordinates......Page 415
7.2.1 Elementary Spherical Waves......Page 419
7.2.2 Properties of the Radial Functions......Page 424
7.2.3 Addition Theorem for the Legendre Polynomials......Page 426
7.2.4 Expansion of Plane Waves......Page 428
7.2.5 Integral Representations......Page 429
7.2.6 A Fourier-Bessel Integral......Page 431
7.2.7 Expansion of a Cylindrical Wave Function......Page 432
7.2.8 Addition Theorem for z_0 (kR)......Page 433
7.3.1 Spherical Vector Wave Functions......Page 434
7.3.2 Integral Representations......Page 436
7.3.3 Orthogonality......Page 437
7.3.4 Expansion of a Vector Plane Wave......Page 438
Problems......Page 440
8.1.1 Kirchhoff Method of Integration......Page 444
8.1.2 Retarded Potentials......Page 448
8.1.3 Retarded Hertz Vector......Page 450
8.2.1 Definition of the Moments......Page 451
8.2.2 Electric Dipole......Page 454
8.2.3 Magnetic Dipole......Page 457
8.3.1 Radiation Field of a Single Linear Oscillator......Page 458
8.3.2 Radiation Due to Traveling Waves......Page 465
8.3.3 Suppression of Alternate Phases......Page 466
8.3.4 Directional Arrays......Page 468
8.3.5 Exact Calculation of the Field of a Linear Oscillator......Page 474
8.3.6 Radiation Resistance by the E.M.F. Method......Page 477
8.4.1 Scalar Wave Functions......Page 480
8.4.2 Direct Integration of the Field Equations......Page 484
8.4.3 Discontinuous Surface Distributions......Page 488
8.5.1 Integration of the Wave Equation......Page 490
8.5.2 Field of a Moving Point Charge......Page 493
Problems......Page 497
9. Boundary - Value Problems......Page 502
9.1.1 Boundary Conditions......Page 503
9.1.2 Uniqueness of Solution......Page 506
9.1.3 Electrodynamic Similitude......Page 508
9.2.1 Snell\'s Laws......Page 510
9.2.2 Fresnel\'s Equations......Page 512
9.2.3 Dielectric Media......Page 514
9.2.4 Total Reflection......Page 517
9.2.5 Refraction in a Conducting Medium......Page 520
9.2.6 Reflection at a Conducting Surface......Page 525
9.3.1 Reflection and Transmission Coefficients......Page 531
9.3.2 Application to Dielectric Media......Page 533
9.3.3 Absorbing Layers......Page 535
9.4.1 Complex Angles of Incidence......Page 536
9.4.2 Skin Effect......Page 540
31534_09b......Page 542
9.5.1 Natural Modes......Page 544
9.5.2 Conductor Embedded in a Dielectric......Page 547
9.5.3 Further Discussion of the Principal Wave......Page 551
9.5.4 Waves in Hollow Pipes......Page 557
9.6.1 Propagation Constant......Page 565
9.6.2 Infinite Conductivity......Page 568
9.6.3 Finite Conductivity......Page 571
9.7.1 Natural Modes......Page 574
9.7.2 Oscillations of a Conducting Sphere......Page 578
9.7.3 Oscillations in a Spherical Cavity......Page 580
9.8.1 Expansion of the Diffracted Field......Page 583
31534_09c......Page 584
9.8.2 Total Radiation......Page 588
9.8.3 Limiting Cases......Page 590
9.9.1 Sommerfeld Solution......Page 593
9.9.2 Weyl Solution......Page 597
9.9.3 Van der Pol Solution......Page 602
9.9.4 Approximation of the Integrals......Page 603
Problems......Page 608
B. Dimensions of Electromagnetic Quantities......Page 620
C. Conversion Tables......Page 621
Formulas from Vector Analysis......Page 623
Conductivity of Various Materials......Page 624
Specific Inductive Capacity of Dielectrics......Page 625
Associated Legendre Functions......Page 627
B......Page 628
C......Page 629
D......Page 631
E......Page 633
F......Page 634
H......Page 635
I......Page 636
L......Page 638
M......Page 639
P......Page 640
R......Page 643
S......Page 645
U......Page 647
W......Page 648
Z......Page 649